Synonymous substitutions substantially improve evolutionary inference from highly diverged proteins.

Codon-and amino acid-substitution models are widely used for the evolutionary analysis of protein-coding DNA sequences. Using codon models, the amounts of both nonsynonymous and synonymous DNA substitutions can be estimated. The ratio of these amounts represents the strength of selective pressure. Using amino acid models, the amount of nonsynonymous substitutions is estimated, but that of synonymous substitutions is ignored. Although amino acid models lose any information regarding synonymous substitutions, they explicitly incorporate the information for amino acid replacement, which is empirically derived from databases. It is often presumed that when the protein-coding sequences are highly divergent, synonymous substitutions might be saturated and the evolutionary analysis may be hampered by synonymous noise. However, there exists no quantitative procedure to verify whether synonymous substitutions can be ignored; therefore, amino acid models have been arbitrarily selected. In this study, we investigate the issue of a statistical comparison between codon-and amino acid-substitution models. For this purpose, we propose a new procedure to transform a 20-dimensional amino acid model to a 61-dimensional codon model. This transformation reveals that amino acid models belong to a subset of the codon models and enables us to test whether synonymous substitutions can be ignored by using the likelihood ratio. Our theoretical results and analyses of real data indicate that synonymous substitutions are very informative and substantially improve evolutionary inference, even when the sequences are highly divergent. Therefore, we note that amino acid models should be adopted only after carefully investigating and discarding the possibility that synonymous substitutions can reveal important evolutionary information.